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Recent work suggests that cross-feeding -- the secretion and consumption ofmetabolic biproducts by microbes -- is essential for understanding microbialecology. Yet how cross-feeding and competition combine to give rise toecosystem-level properties remains poorly understood. To address this question,we analytically analyze the Microbial Consumer Resource Model (MiCRM), aprominent ecological model commonly used to study microbial communities. Ourmean-field solution exploits the fact that unlike replicas, the cavity methoddoes not require the existence of a Lyapunov function. We use our solution toderive new species-packing bounds for diverse ecosystems in the presence ofcross-feeding, as well as simple expressions for species richness and theabundance of secreted resources as a function of cross-feeding (metabolicleakage) and competition. Our results show how a complex interplay betweencompetition for resources and cooperation resulting from metabolic exchangecombine to shape the properties of microbial ecosystems.

Cross-feeding shapes both competition and cooperation in microbial ecosystems